I'm fairly new to the Civ series, I played very little Civ 2, 3 and almost none of 4, but I'll tell you what I played a metric TON of back in the day: Master of Orion 2. The two games are somewhat similar, I'd say MOO2 is less involved, but something it did interestingly (you'll pardon any awkward grammar, I just got done with a 4 hour Civ V session...) was let you create your own race. Each race had certain attributes and when you created your own, it assigned a positive or negative point cost to each attribute, allowing you to start with 10 and go up to 20 points. 
Long story short, do you think this could've been somehow implemented in the Civ series? As a follow-up: if they'd included this in Civ V, I assume just allowing you to cherry-pick two passive advantages and two unique units, what would you have chosen?

A big draw and even the tone of Civ 5 is grounded in it's application of real world history. All the bonuses are trying to be as faithful to things that civilization actually did. plus the challenge of not being able to choose your bonuses is part of the experience.

Wait for a mod? 
In a world where you can pick your own perks, someone finds an exploit and now everyone's making the same custom character. There's a lot of nuance to balance here, its not an MMO where you're just clicking on the thing you want to die.

Seeing as theres the option to load a mod on the main menu, the OP just has to find where he can download the mod maker if its free so he can just make his own overpowered mod and think he's good when he wins with them.  
 
But seriously, no civ is perfect because in real life no civ is perfect. Its all up to you to use thier strengths to hide thier weaknesses. 

There are actually already a few mods for new races. 
 
I was VERY happy when I found out someone made a Celtic Civilization as after a few hours of Civ V it was the one thing I was wishing for. 
 
I understand the Mod Tools are fairly easy to pick up so perhaps you could make your own mod! Like say...a GiantBomb Civ? That would be all kinds of entertaining.

...so I got a hunch new Civs will be in DLC and/or Expansions?

Probably, did anyone else get the Steam Edition so they could get Babylon? I have a Marathon game going right now where I placed Babylon EXACTLY between it's two rivers, I was pretty proud of myself for that one.

Sheesh, people just assume I wanna powergame my way through this or that I'm somehow discontented with the balance. I love the balance and I hate powergaming (no challenge means what's the point?) It was more just to see what kind of crazy combinations you could've come up with. I really don't think the any advantages and units are so amazingly good that if you combined them all, you'd be unstoppable. Also, created nations could be outlawed in multi-player games in case the weird situation came up where there WAS some crazy-powerful combination (as I'm sure someone somewhere would find out as quickly as they could).

" ...so I got a hunch new Civs will be in DLC and/or Expansions? "

" There are actually already a few mods for new races.  I was VERY happy when I found out someone made a Celtic Civilization as after a few hours of Civ V it was the one thing I was wishing for.  I understand the Mod Tools are fairly easy to pick up so perhaps you could make your own mod! Like say...a GiantBomb Civ? That would be all kinds of entertaining. "

I was kinda wondering how they choose Civs for the game, I was thinking of getting it so might play as the Celtic Civ the other guy mentioned if I do. Does each Civ have a leader that stays the same forever? As in they wouldn't die over time.

"I was kinda wondering how they choose Civs for the game, I was thinking of getting it so might play as the Celtic Civ the other guy mentioned if I do. Does each Civ have a leader that stays the same forever? As in they wouldn't die over time. "

The leader for the Celtic Civ was not a name I recalled from my personal studies of Celtic mythology, granted@eroticfishcake said:

" @IrishCoffee said:

" There are actually already a few mods for new races.  I was VERY happy when I found out someone made a Celtic Civilization as after a few hours of Civ V it was the one thing I was wishing for.  I understand the Mod Tools are fairly easy to pick up so perhaps you could make your own mod! Like say...a GiantBomb Civ? That would be all kinds of entertaining. "

Who was the leader of the Celtic Civ? Don't tell me it's Cowell...or Bertie...or anyone for that matter. "

There was a mod in Civ4 called Rhye's and Fall of Civilization that was absolutely amazing for historical accuracy.  Historical start locations, every civ had a special historical win condition, and every civ actually spawned at the right time frame (So you don't start in 4,000 BC unless you're an ancient civilization.  If you play say, America, the game plays itself until you reach the spawn time at 1776 AD).  So that somewhat addresses the immortal leader thing and the weirdness of playing America in 4,000 BC. 
 
Dunno if there's any word about Rhye doing a mod for Civ5 or not.

Assuming my simple mind can learn the program, I plan to use the mod tools to make the Canada civilization. Tired of always have to play as England and using my imagination to make it Canada. I think our power will be a health care system that causes your cities to require half the food to create new citizens, and a special AoE artillery unit for the WW2 era or a sniper unit that has a good long range attack/movement but is only effective against human units.